What is the fastest way to texture bake a full scene?
Depending on your intended volume either by doing it manually or making a script that handles the bake. 

You will need to manage at least the following:


texture resolution for each baked mesh object
which objects to bake (you probably don't want to bake glass / transparent objects / illuminating surfaces / gfx like light halos etc
setting up lightmap bake UV layer (most likely you have the default UV used for getting the texture itself tiling correctly)
setting up an image texture node for every material in the object being baked and make a new image for it and make the node selected
saving the texture on disk with naming convention that allows you to read the images into a new, realtime baked materials that correspond to the mesh objects when you start BGE


If you plan on making more than 1 or 2 levels, to me it definitely calls for script assistance.